Problem: Solve for $x$ and $y$ using elimination. ${-3x+5y = 15}$ ${3x+2y = 27}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $7y = 42$ $\dfrac{7y}{{7}} = \dfrac{42}{{7}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-3x+5y = 15}\thinspace$ to find $x$ ${-3x + 5}{(6)}{= 15}$ $-3x+30 = 15$ $-3x+30{-30} = 15{-30}$ $-3x = -15$ $\dfrac{-3x}{{-3}} = \dfrac{-15}{{-3}}$ ${x = 5}$ You can also plug ${y = 6}$ into $\thinspace {3x+2y = 27}\thinspace$ and get the same answer for $x$ : ${3x + 2}{(6)}{= 27}$ ${x = 5}$